Thanks for the reply. My question is, generally, what are those things - "there's a few things that allow/disallow/forcefully allow it, depending on the situation". I understand you need to have open borders with the other civilization, but is there more you need to do as in actually offer to share trade routes with them? Thanks again for the help.
Writing tech is required to sign Open Borders and start foreign trade routes. They aren't a visible mechanic (like assigning units to run the route such as in AoE or similar) in the game but are instead a sort of free commerce generated by each city that has routes set up with other cities.
You can view them under the city summary screen to the top left:
Trade routes automatically set themselves up so long as you have a connection between cities. Theres a whole bunch that goes into the way it selects the specific routes...I understand it generally searches for the "best" route -- routes across longer distances, between larger cities, between different landmasses all give more commerce. But for routes internal or foreign, routes only set up between
connected cities.
In the case of foreign cities, Open Borders agreements are a prereq too. You can trade resources but not earn commerce off foreign routes unless you have open borders. This means being at war also precludes trade route with rivals (the one(s) at war with you), and they are automatically cancelled and recalculated elsewhere when wars interrupt trade.
Cities are most commonly linked up through either road networks, or along coasts/down rivers when you have the Sailing tech. It's also possible to link cities without Sailing if every river/coast tile between the two cities is completely within your borders. Last, Astronomy tech allows any cites with coastal connections to link to one another across the oceans; these trade routes are more lucrative because they are always boosted by way of being intercontinental.
The simplest way to see it in action is to create a road network linking your own cities. Every city connected on the network can trade back with at least the capitol. If you connect into a foreign rival's road network by building a road on a tile that connects to one of theirs, if you have Open Borders you can see the routes in your cities swap over to more lucrative foreign routes.
By default cities can only run a single trade route.. Techs like Currency, Corporation, the civic Free Market, the Great Lighthouse wonder, a UN resolution etc. can increase the number of trade routes each city can run.